Problem: Let $f(x) = -x^{2}-9x+1$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Solution: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-x^{2}-9x+1 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -1, b = -9, c = 1$ $ x = \dfrac{+ 9 \pm \sqrt{(-9)^{2} - 4 \cdot -1 \cdot 1}}{2 \cdot -1}$ $ x = \dfrac{9 \pm \sqrt{85}}{-2}$ $ x = \dfrac{9 \pm \sqrt{85}}{-2}$ $x =\dfrac{9 \pm \sqrt{85}}{-2}$